There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Magic Matrix

Stage: 2 Challenge Level:

Several of you noticed that the numbers you
end up with in the matrix always add up to 10 - to fit in with
NRICH's 10th anniversary! A whole group of pupils from Gorseland
Primary School worked hard on the first matrix in pairs,
discovering how it works, making their own and solving this
problem. They found this solution for the first matrix:

George from Greenwich solved the second and
third matrices as well. For the second one, he says:

The numbers on the sides are the eight magic numbers, they are 1.7,
0.3, 0.1, 2.6, 0.2, 1.7, 1 and 2.4. The eight numbers add up to 10
and they fit in place:

0.2

1.7

1

2.4

1.7

1.9

3.4

2.7

4.1

0.3

0.5

2

1.3

2.7

0.1

0.3

1.8

1.1

2.5

2.6

2.8

4.3

3.6

5

For the third matrix, George
says:

What you have to do in the first step is convert all the fractions
to a common denominator to make it easier. The common number is 12.
This is the solved grid below. As you can see, the eight numbers
are 8/12, 6/12, 19/12, 27/12, 5/12, 9/12, 30/12 and 16/12. They add
up to 10 as well.

6/12

19/12

27/12

5/12

8/12

14/12

27/12

35/12

13/12

9/12

15/12

28/12

36/12

14/12

30/12

36/12

49/12

57/12

35/12

16/12

22/12

35/12

43/12

21/12

You can check that this is the same as
the matrix in the problem! Excellent George, thank you for sending
in your solutions.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.